The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  1  1  1  1  1  X  0  1  1  X
 0  X  0 X^2+X  0 X^2+X  0 X^2+X X^2 X^2+X  0  0 X^2+X  X X^2+X  0 X^2 X^2  0 X^2 X^2+X  X X^2+X X^2+X  0
 0  0 X^2  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2
 0  0  0 X^2  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2
 0  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2
 0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0
 0  0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0

generates a code of length 25 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+72x^20+72x^22+128x^23+130x^24+256x^25+80x^26+128x^27+100x^28+40x^30+11x^32+4x^36+2x^40

The gray image is a linear code over GF(2) with n=100, k=10 and d=40.
This code was found by Heurico 1.16 in 0.0289 seconds.